Question

In: Statistics and Probability

The maximum reaction rates (Vmax) for the enzyme invertase were measured from samples at four temperatures....

The maximum reaction rates (Vmax) for the enzyme invertase were measured from samples at four temperatures. Test the hypothesis that there are no significant differences in the mean invertase reaction rates among temperatures at the 5% level of significance. (8 points)

Vmax for Inveratse (10–3 mM/min)

30C

40C

50C

60C

2.3

2.6

2.9

2.8

2.9

3.2

3.5

3.4

2.2

2.4

4.2

2.6

2.5

3.2

2.6

3.2

1. What type of Analysis should you conduct to solve this problem? a. Two-Factor ANOVA b. One-Factor ANOVA c. Paired t-test d. Independent t-test

2. What are the sample sizes for each group? (n1, n2, n3, n4) a. 5, 4, 3, 4 b. 5, 8, 12, 8 c. 4, 5, 3, 4 d. 5, 4, 4, 3

3. What is the total sample size? a. 4 b. 5 c. 16 d. 12

4. What is the total average? a. 2.9840 b. 2.7640 c. 2.9063 d. 2.6500

5. What is the total Sum of all observations? a. 46.5 b. 34.0 c. 54.6 d. 45.2

6. Report the SS(group) value. a. 1.0778 b. 1.9578 c. 3.9520

Solutions

Expert Solution

One - Factor ANOVA we should conduct to solve this problem.

H0: Null Hypothesis: ( there are no significant differences in the mean invertase reaction rates among temperatures ) (Claim)

HA: Alternative Hypothesis: ( there are significant differences in the mean invertase reaction rates among temperatures )

From the given data,the following Table is calculated:

Temperature N Mean Std. Dev.
300 C 5 2.62 0.4207
400 C 4 2.85 0.4123
500 C 4 3.30 0.7071
600 C 3 2.9333 0.4163

From the above Table, ANOVA Table is calculated as follows:

Source of Variation Degrees of Freedom Sum of Squares Mean Square F P Value
Between Groups 3 1.0447 1.0447/3=0.3482 0.3482/0.2554=1.3636 0.3008
WithinGroups 12 3.0645 3.0645/12=0.2554
Total 15 4.1092

Test Statistic is given by:
F = 0.3482/0.2554=1.3636

Degrees of Freedom for numerator =3

Degrees of Freedom for denominaor = 12

By Technology, P - Value = 0.3008

Since P - value = 0.3008 is greater than = 0.05, the difference is not significant. Fail to rejectnull hypothesis.

Conclusion:
The data support the claim that there are no significant differences in the mean invertase reaction rates among temperatures.

Answersto questions asked:

1.   Question:

What type of Analysis should you conduct to solve this problem?

Correct option:

b. One-Factor ANOVA

2.    Question:

What are the sample sizes for each group? (n1, n2, n3, n4)

Correct option:

d. 5, 4, 4, 3

3     Question:

What is the total sample size?

Correct option:

c. 16

4    Question:

What is the total average?

Correct option:

c. 2.9063

Explanation:

Total average = the total Sum of all observations / the total sample size = 46.5/16 = 2.9063

5. Question:

What is the total Sum of all observations?

Correct option:

a. 46.5

6. Question:

Report the SS(group) value

Correct option:

a. 1.0778

orchestra answered 2 years ago
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